Measuring the propagation speed of gravitational waves with LISA

The propagation speed of gravitational waves, c , has been tightly constrained by the binary neutron star merger GW170817 and its electromagnetic counterpart, under the assumption of a frequency-independent c . Drawing upon arguments from Effective Field Theory and quantum gravity, we discuss the possibility that modifications of General Relativity allow for transient deviations of c from the speed of light at frequencies well below the band of current ground-based detectors. We motivate two representative Ansätze for c (f), and study their impact upon the gravitational waveforms of massive black hole binary mergers detectable by the LISA mission. We forecast the constraints on c (f) obtainable from individual systems and a population of sources, from both inspiral and a full inspiral-merger-ringdown waveform. We show that LISA will enable us to place stringent independent bounds on departures from General Relativity in unexplored low-frequency regimes, even in the absence of an electromagnetic counterpart.